起重机仿生箱梁结构局部稳定性设计理论研究
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摘要
起重机结构自重大,运行能耗高,其结构轻量化是实现节能降耗的重要手段。以往结构轻量化设计主要针对结构参数优化,或采用高强度钢进行材料替代。在现有结构设计理论基础上,要进一步降低结构件质量,提高结构件的承力性能必须找到新的结构设计方法和思路。针对起重机箱梁结构轻量化的科学问题,从结构仿生学相似性原理出发,提出叶脉加劲肋结构形式,通过研究叶脉及竹节的自然分布特性,指导加劲肋在箱梁结构中的仿生布置设计。
针对斜向肋箱梁结构中的局部屈曲失稳问题,推导斜坐标系下简支边弯矩计算公式、纵向面内载荷作用下斜板的屈曲平衡微分方程,将调和微分求积法和边界融入法结合起来,给出调和边界融入微分求积法求解简支斜板局部稳定性的具体方法。以单向轴压和剪应力作用下简支斜板为例,研究载荷变化系数、斜板边长比和倾角同屈曲临界载荷之间的关系。结果表明：单向轴压作用下简支斜板屈曲临界载荷随载荷变化系数的增大而增大、随倾角的增大而减小、随边长比的增大先增大后减小再增大；剪应力作用下简支斜板屈曲临界载荷随边长比的增大而增大、随倾角的增大先减小后增大。以双向轴压或单向轴压与剪应力作用下简支斜板为例,研究载荷比值(1／5≤Ny/Nx≤5,或1／5≤Nxy／Nx≤5)、斜板边长比(1／2≤ 针对非均布载荷作用下矩形板件的屈曲承载力问题,从几何形状、边界条件和载荷三个角度,研究局部受载弹性薄板的对称特性。运用有限元求解具有对称性矩形板的屈曲临界载荷,并通过对比DQM数值解验证有限元解的精确性。同时对比非均布载荷作用下矩形板屈曲临界载荷的传统经验公式,给出能够满足工程实际需要的修正经验公式。
以竹子为仿生对象对正轨箱梁横向肋进行结构优化设计。通过研究竹子结构特征参数的自然分布特性与受力特性间的作用关系,发现不同受力截面对应不同的等效节间距。考虑加劲肋间距对结构刚度和强度指标的影响,设定加劲肋极限间距。建立正轨箱梁加劲肋变间距等稳定性优化策略,结合有限元弹性屈曲分析进行迭代优化,实现加劲肋变间距等稳定性设计。经实例研究表明,优化求解速率随偏差率增大而增大；仿生箱梁较传统箱梁加劲肋数量由15道减小为10道、主梁重量减轻；各截面屈曲抗失稳能力差异减小,同时满足强度和刚度指标设计要求。
本文从理论角度、数值仿真和有限元仿真三个角度,针对仿生斜向肋箱梁结构中局部斜板的屈曲承载力问题进行了系统研究。同时,针对仿生变间距肋正轨箱梁进行了等稳定性设计。论文研究工作具有较强的理论意义和实用价值,为后续的研究工作奠定了坚实的基础。
The weight of crane's structure is heavy, which leads to great energy consumption, the lightweight design of crane's structure is an efficent method to to save energy. In the previous work on the crane's lightweight design, there are mainly about the optimum for structure parameters and using the high-strength steel as alternate material. Based on the present optimum methods about the lightweight design of crane's structure, creative method and idea is necessary to get a further light weight of the crane's structure. Aiming at the scientific problem on the lightweight design for the box girder structure, the leaf vein stiffener structure is proposed by the structure bionics similarity principle. The bionics arrangement for the leaf vein stiffener in the box girder structure is carried out by studying the natural distribution property of the leaf vein and bamboo node.
To investigate the buckling of skew plates for the crane's box girder, the equations of moment for simply supported edges are given, besides, the bucking differential governing equations for skew plates is also given when it is subjected to the in-plane loading. And the calculation procedures are described in detail when the harmonic differential quadrature methods combining with Build-in methods are used to solve the critical buckling load of simply supported skew plates. Skew plates subjected to the uniaxial pressure or shear force is considered as the case study, the affecting relation between the critical buckling load and parameters for skew plates is discussed, and the parameters include the coefficient of linearly varying uniaxial pressure k ranging from0to2, the aspect ratio ranging from0.5to2and skew angles ranging from30°to90°. It is shown that when skew plates are subjected to the uniaxial pressure, the critical buckling load increases with the increasing of the coefficient of linearly varying uniaxial pressure k, and it increases with the decreasing of skew angles, however, it increases first and then decreases and finally increases with the increasing of the aspect ratio. When skew plates are subjected to the shear force, the critical buckling load increases with the increasing of the aspect ratio, and it decreases first and then increases with the increasing of skew angles. Skew plates subjected to the biaxial pressure or uiaxial pressure combined with shear force is considered as the case study, the affecting relation between the critical buckling load and parameters for skew plates is discussed, and the parameters include the ratio of Ny to Ax or Nxy/Nx ranging from1/5to5, the aspect ratio r ranging from0.5to2and skew angles ranging from30°to90°. For skew plates subjected to the biaxial pressure, it is shown that the critical buckling load decreases with the increasing of the ratio of Ny,to Nx, it increases with the increasing of aspect ratio, and it decreases with the increasing of the skew angle. For skew plates subjected to uiaxial pressure combined with shear force, it is shown that the critical buckling load decreases with the increasing of the ratio of Nxy/Nx, it increases or decreases with the increasing of the aspect ratio ranging from1/2to1when the skew angle is in different value, it increases with the increasing of the aspect ratio ranging from1to2, and it decreases with the increasing of the skew angles. Skew plates with the boundary condition, CCCC, CSCS or SCSC, subjected to the uniaxial pressure or shear force is considered as the case study, the affecting relation between the critical buckling load and parameters for skew plates is discussed, and the parameters include the aspect ratio and skew angles. It is shown that when skew plates with the boundary condition, CCCC or CSCS, are subjected to the uniaxial pressure, the critical buckling load increases with the increasing of the aspect ratio, and it decreases with the increasing of skew angles. However, when skew plates with the boundary condition, SCSC, are subjected to the uniaxial pressure, the critical buckling load fluctuates with the increasing of the aspect ratio, and it decreases with the increasing of skew angles. It is also shown that when skew plates with the boundary condition, SCSC, are subjected to the shear force, the critical buckling load increases with the increasing of the aspect ratio, and it decreases first and then increases with the increasing of skew angles.
For the critical buckling load of rectangular plates subjected to nonlinear load, the asymmetrical characteristic is investigated in three ways, geometry shape, boundary and load conditions. The FEM is used to solve the critical buckling load of the rectangular plates with the asymmetrical characteristic. At the same tine, results got by FEM is compared with the DQM to verify the accuracy of the numerical solutions. A modified formula is given for the critical buckling load rectangular plates subjected to nonlinear load, which can meet the demand for the engineering design.
The bamboo was selected as the bionics objectives, and the structure optimum was made about the transverse stiffener in the upright rail box girder. The research on the affecting relationship was made for the bamboo between the nature distribution and mechanical behaviors. It is shown that different cross sections correspond to different equivalent distances between two adjacent nodes. The effect of distances between two adjacent stiffeners on the structure rigidity and strength index was analyzed, and the maximum distances between two adjacent stiffeners can be set. The optimum law was built to make the stiffener be of the changeable distance and same stability. The iteration optimum of the buckling analysis was done by the finite method, and finally the stiffener has the changeable distance and same stability. Several conclusions are got by the case study for the bionics design. The optimum solution speed increases by the increasing of the bias proportion. As compared with the traditional box girder, the number of stiffeners in the bionics box girder decreases from15to10, which makes the weight of main beams decrease. Besides, the bionics box girder has more uniform buckling load-bearing ability, the design demand of rigidity and strength index can be met.
By using the mechanics theory, numerical simulation and FEM simulation, respectively, the critical buckling load for skew plates in the bionics box girder is systematically analyzed, at the same time, the same stability design for the in the upright rail box girder is also made. The research work are of great value on both theory and engineering practice, and have provided a basis for our further research.
针对斜向肋箱梁结构中的局部屈曲失稳问题,推导斜坐标系下简支边弯矩计算公式、纵向面内载荷作用下斜板的屈曲平衡微分方程,将调和微分求积法和边界融入法结合起来,给出调和边界融入微分求积法求解简支斜板局部稳定性的具体方法。以单向轴压和剪应力作用下简支斜板为例,研究载荷变化系数、斜板边长比和倾角同屈曲临界载荷之间的关系。结果表明：单向轴压作用下简支斜板屈曲临界载荷随载荷变化系数的增大而增大、随倾角的增大而减小、随边长比的增大先增大后减小再增大；剪应力作用下简支斜板屈曲临界载荷随边长比的增大而增大、随倾角的增大先减小后增大。以双向轴压或单向轴压与剪应力作用下简支斜板为例,研究载荷比值(1／5≤Ny/Nx≤5,或1／5≤Nxy／Nx≤5)、斜板边长比(1／2≤
以竹子为仿生对象对正轨箱梁横向肋进行结构优化设计。通过研究竹子结构特征参数的自然分布特性与受力特性间的作用关系,发现不同受力截面对应不同的等效节间距。考虑加劲肋间距对结构刚度和强度指标的影响,设定加劲肋极限间距。建立正轨箱梁加劲肋变间距等稳定性优化策略,结合有限元弹性屈曲分析进行迭代优化,实现加劲肋变间距等稳定性设计。经实例研究表明,优化求解速率随偏差率增大而增大；仿生箱梁较传统箱梁加劲肋数量由15道减小为10道、主梁重量减轻；各截面屈曲抗失稳能力差异减小,同时满足强度和刚度指标设计要求。
本文从理论角度、数值仿真和有限元仿真三个角度,针对仿生斜向肋箱梁结构中局部斜板的屈曲承载力问题进行了系统研究。同时,针对仿生变间距肋正轨箱梁进行了等稳定性设计。论文研究工作具有较强的理论意义和实用价值,为后续的研究工作奠定了坚实的基础。
The weight of crane's structure is heavy, which leads to great energy consumption, the lightweight design of crane's structure is an efficent method to to save energy. In the previous work on the crane's lightweight design, there are mainly about the optimum for structure parameters and using the high-strength steel as alternate material. Based on the present optimum methods about the lightweight design of crane's structure, creative method and idea is necessary to get a further light weight of the crane's structure. Aiming at the scientific problem on the lightweight design for the box girder structure, the leaf vein stiffener structure is proposed by the structure bionics similarity principle. The bionics arrangement for the leaf vein stiffener in the box girder structure is carried out by studying the natural distribution property of the leaf vein and bamboo node.
To investigate the buckling of skew plates for the crane's box girder, the equations of moment for simply supported edges are given, besides, the bucking differential governing equations for skew plates is also given when it is subjected to the in-plane loading. And the calculation procedures are described in detail when the harmonic differential quadrature methods combining with Build-in methods are used to solve the critical buckling load of simply supported skew plates. Skew plates subjected to the uniaxial pressure or shear force is considered as the case study, the affecting relation between the critical buckling load and parameters for skew plates is discussed, and the parameters include the coefficient of linearly varying uniaxial pressure k ranging from0to2, the aspect ratio ranging from0.5to2and skew angles ranging from30°to90°. It is shown that when skew plates are subjected to the uniaxial pressure, the critical buckling load increases with the increasing of the coefficient of linearly varying uniaxial pressure k, and it increases with the decreasing of skew angles, however, it increases first and then decreases and finally increases with the increasing of the aspect ratio. When skew plates are subjected to the shear force, the critical buckling load increases with the increasing of the aspect ratio, and it decreases first and then increases with the increasing of skew angles. Skew plates subjected to the biaxial pressure or uiaxial pressure combined with shear force is considered as the case study, the affecting relation between the critical buckling load and parameters for skew plates is discussed, and the parameters include the ratio of Ny to Ax or Nxy/Nx ranging from1/5to5, the aspect ratio r ranging from0.5to2and skew angles ranging from30°to90°. For skew plates subjected to the biaxial pressure, it is shown that the critical buckling load decreases with the increasing of the ratio of Ny,to Nx, it increases with the increasing of aspect ratio, and it decreases with the increasing of the skew angle. For skew plates subjected to uiaxial pressure combined with shear force, it is shown that the critical buckling load decreases with the increasing of the ratio of Nxy/Nx, it increases or decreases with the increasing of the aspect ratio ranging from1/2to1when the skew angle is in different value, it increases with the increasing of the aspect ratio ranging from1to2, and it decreases with the increasing of the skew angles. Skew plates with the boundary condition, CCCC, CSCS or SCSC, subjected to the uniaxial pressure or shear force is considered as the case study, the affecting relation between the critical buckling load and parameters for skew plates is discussed, and the parameters include the aspect ratio and skew angles. It is shown that when skew plates with the boundary condition, CCCC or CSCS, are subjected to the uniaxial pressure, the critical buckling load increases with the increasing of the aspect ratio, and it decreases with the increasing of skew angles. However, when skew plates with the boundary condition, SCSC, are subjected to the uniaxial pressure, the critical buckling load fluctuates with the increasing of the aspect ratio, and it decreases with the increasing of skew angles. It is also shown that when skew plates with the boundary condition, SCSC, are subjected to the shear force, the critical buckling load increases with the increasing of the aspect ratio, and it decreases first and then increases with the increasing of skew angles.
For the critical buckling load of rectangular plates subjected to nonlinear load, the asymmetrical characteristic is investigated in three ways, geometry shape, boundary and load conditions. The FEM is used to solve the critical buckling load of the rectangular plates with the asymmetrical characteristic. At the same tine, results got by FEM is compared with the DQM to verify the accuracy of the numerical solutions. A modified formula is given for the critical buckling load rectangular plates subjected to nonlinear load, which can meet the demand for the engineering design.
The bamboo was selected as the bionics objectives, and the structure optimum was made about the transverse stiffener in the upright rail box girder. The research on the affecting relationship was made for the bamboo between the nature distribution and mechanical behaviors. It is shown that different cross sections correspond to different equivalent distances between two adjacent nodes. The effect of distances between two adjacent stiffeners on the structure rigidity and strength index was analyzed, and the maximum distances between two adjacent stiffeners can be set. The optimum law was built to make the stiffener be of the changeable distance and same stability. The iteration optimum of the buckling analysis was done by the finite method, and finally the stiffener has the changeable distance and same stability. Several conclusions are got by the case study for the bionics design. The optimum solution speed increases by the increasing of the bias proportion. As compared with the traditional box girder, the number of stiffeners in the bionics box girder decreases from15to10, which makes the weight of main beams decrease. Besides, the bionics box girder has more uniform buckling load-bearing ability, the design demand of rigidity and strength index can be met.
By using the mechanics theory, numerical simulation and FEM simulation, respectively, the critical buckling load for skew plates in the bionics box girder is systematically analyzed, at the same time, the same stability design for the in the upright rail box girder is also made. The research work are of great value on both theory and engineering practice, and have provided a basis for our further research.
引文
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